arXiv 2005.122002020-05quant-ph

随机参数化量子线路中通过关联的大梯度

Large gradients via correlation in random parameterized quantum circuits

Tyler Volkoff, Patrick J. Coles

备注：: 21 pages, 3 figures
发表信息：: Quantum Sci. Technol. 6, 025008 (2021)
DOI：: 10.1088/2058-9565/abd891

摘要：

变分量子算法的规模大的问题的大小，需要有效的随机参数化量子线路的优化。对于具有不相关参数的此类电路，成本函数景观中指数消失梯度的存在是梯度下降法优化的障碍。在这项工作中，我们证明，通过利用包含空间或时间相关的门层的电路模块，降低参数空间的维数可以允许规避消失的梯度现象。例子来自随机可分离电路和渐近最优变分版本的Grover算法的基础上的量子交替算子anomaly（QAOA）。在后一种情况下，我们对成本函数变化的限制意味着随着层数向$\mathcal{O}(2^{n/2})$（量子非结构化搜索的最佳预言复杂度）增加，梯度消失和有效可训练性之间的过渡。

英文摘要：

Scaling of variational quantum algorithms to large problem sizes requires efficient optimization of random parameterized quantum circuits. For such circuits with uncorrelated parameters, the presence of exponentially vanishing gradients in cost function landscapes is an obstacle to optimization by gradient descent methods. In this work, we prove that reducing the dimensionality of the parameter space by utilizing circuit modules containing spatially or temporally correlated gate layers can allow one to circumvent the vanishing gradient phenomenon. Examples are drawn from random separable circuits and asymptotically optimal variational versions of Grover's algorithm based on the quantum alternating operator ansatz (QAOA). In the latter scenario, our bounds on cost function variation imply a transition between vanishing gradients and efficient trainability as the number of layers is increased toward $\mathcal{O}(2^{n/2})$, the optimal oracle complexity of quantum unstructured search.

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